Adaptation of the Vogt–Mizaikoff F‐test to determine the number of principal factors responsible for a data matrix and comparison with other popular methods

The use of principal component regression, a multivariate calibration method, in the analysis of in vivo fast-scan cyclic voltammetry data allows for separation of overlapping signal contributions, permitting evaluation of the temporal dynamics of multiple neurotransmitters simultaneously. To accomplish this, the technique relies on information about current-concentration relationships across the scan-potential window gained from analysis of training sets. The ability of the constructed models to resolve analytes depends critically on the quality of these data. Recently, the use of standard training sets obtained under conditions other than those of the experimental data collection (e.g., with different electrodes, animals, or equipment) has been reported. This study evaluates the analyte resolution capabilities of models constructed using this approach from both a theoretical and experimental viewpoint. A detailed discussion of the theory of principal component regression is provided to inform this discussion. The findings demonstrate that the use of standard training sets leads to misassignment of the current-concentration relationships across the scan-potential window. This directly results in poor analyte resolution and, consequently, inaccurate quantitation, which may lead to erroneous conclusions being drawn from experimental data. Thus, it is strongly advocated that training sets be obtained under the experimental conditions to allow for accurate data analysis.

show abstract

“…Estimates place this transition for the Malinowski’s F-test between signal-to-noise ratios of 10–100. 33 …”

Section: Theorymentioning

confidence: 99%

Failure of Standard Training Sets in the Analysis of Fast-Scan Cyclic Voltammetry Data

Johnson

Rodeberg

Wightman

2016

ACS Chem. Neurosci.

View full text Add to dashboard Cite

show abstract

“…[20, 25] Through simulations of random matrices error REVs were determined not to follow a normal distribution when r and c deviated substantially from one another[24] which violate the assumption necessary for an F -test, but Malinowski’s F -test has been used successfully to estimate the rank of these “skinny” matrices in the literature. [25, 26]…”

Section: Theorymentioning

confidence: 99%

Rank Estimation and the Multivariate Analysis of in Vivo Fast-Scan Cyclic Voltammetric Data

2010

View full text Add to dashboard Cite

Principal component regression has been used in the past to separate current contributions from different neuromodulators measured with in vivo fast-scan cyclic voltammetry. Traditionally, a percent cumulative variance approach has been used to determine the rank of the training set voltammetric matrix during model development, however this approach suffers from several disadvantages including the use of arbitrary percentages and the requirement of extreme precision of training sets. Here we propose that Malinowski's F-test, a method based on a statistical analysis of the variance contained within the training set, can be used to improve factor selection for the analysis of in vivo fast-scan cyclic voltammetric data. These two methods of rank estimation were compared at all steps in the calibration protocol including the number of principal components retained, overall noise levels, model validation as determined using a residual analysis procedure, and predicted concentration information. By analyzing 119 training sets from two different laboratories amassed over several years, we were able to gain insight into the heterogeneity of in vivo fast-scan cyclic voltammetric data and study how differences in factor selection propagate throughout the entire principal component regression analysis procedure. Visualizing cyclic voltammetric representations of the data contained in the retained and discarded principal components showed that using Malinowski's F-test for rank estimation of in vivo training sets allowed for noise to be more accurately removed. Malinowski's F-test also improved the robustness of our criterion for judging multivariate model validity, even though signal-to-noise ratios of the data varied. In addition, pH change was the majority noise carrier of in vivo training sets while dopamine prediction was more sensitive to noise.

show abstract

“…Various chemometric techniques such as the factor indicator function, F-tests for establishing significance levels, distribution of misfit, x 2 -tests, cross validation, etc., have been developed to estimate the rank of matrices in the absence of such information. Table I is a compilation of some of the more popular methods [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. It lists the various selection criteria involved as well as comments concerning requirements, assumptions, limitations or applicability.…”

Section: Introductionmentioning

confidence: 99%

Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix

Malinowski

2008

Journal of Chemometrics

Self Cite

View full text Add to dashboard Cite

Median absolute deviation (MAD) is a well-established statistical method for determining outliers. This simple statistic can be used to determine the number of principal factors responsible for a data matrix by direct application to the residual standard deviation (RSD) obtained from principal component analysis (PCA). Unlike many other popular methods the proposed method, called determination of rank by MAD (DRMAD), does not involve the use of pseudo degrees of freedom, pseudo F-tests, extensive calibration tables, time-consuming iterations, nor empirical procedures. The method does not require strict adherence to normal distributions of experimental uncertainties. The computations are direct, simple to use and extremely fast, ideally suitable for online data processing. The results obtained using various sets of chemical data previously reported in the chemical literature agree with the early work. Limitations of the method, determined from model data, are discussed. An algorithm, written in MATLAB format, is presented in the Appendix.

show abstract

Adaptation of the Vogt–Mizaikoff F‐test to determine the number of principal factors responsible for a data matrix and comparison with other popular methods

Cited by 14 publications

References 10 publications

Failure of Standard Training Sets in the Analysis of Fast-Scan Cyclic Voltammetry Data

Failure of Standard Training Sets in the Analysis of Fast-Scan Cyclic Voltammetry Data

Rank Estimation and the Multivariate Analysis of in Vivo Fast-Scan Cyclic Voltammetric Data

Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix

Contact Info

Product

Resources

About